If cos (α + β) = 0 then sin (α – β) = ?

Given: cos(α + β) = 0

As we know that,

$\cos 90^{\circ}=0$

Since, $\cos (\alpha+\beta)=0$

$\Rightarrow \alpha+\beta=90^{\circ}$

$\Rightarrow \alpha=90^{\circ}-\beta \quad \ldots(1)$

Now,

$\sin (\alpha-\beta)=\sin \left(90^{\circ}-\beta-\beta\right)$

$=\sin \left(90^{\circ}-2 \beta\right)$

$=\cos 2 \beta \quad\left(\because \sin \left(90^{\circ}-\theta\right)=\cos \theta\right)$

Hence, the correct option is (b).